Berechnung von mittleren Schwingungsamplituden einiger tetraedrischer Moleküle und Ionen nach der Methode der charakteristischen Schwingungen

Mean amplitudes of vibration of a series of tetrahedralXY ₄ molecules and ions (hydrides, halides, oxides and oxoanions) have been calculated using the “Method of the Characteristic Vibrations” ofA. Müller. The results indicate that this method leads to very good values for most of the investigated species, and especially in the cases of highM _X/M_Y mass ratio.     

Untersuchung der Temperaturabhängigkeit der kernmagnetischen Spin-Gitter-Relaxation an Dimethylsiloxanen

Zusammenfassung Es wurden die longitudinalen Protonen-RelaxationszeitenT ₁ der beiden Systeme Hexamethyldisiloxan und Dekamethylcyclopentasiloxan im Temperaturbereich von 20 bis 300 K untersucht. Das Relaxationsverhalten des Hexamethyldisiloxans wird in diesem Temperaturbereich durch drei Bewegungsmechanismen bestimmt: die Methylgruppenrotation um die C₃-Achse, die Segmentrotation um die Si-O-Bindung und einen noch nicht näher identifizierten Bewegungsprozeß, der zu einer sprunghaften Änderung der Spin-Gitter-Relaxationszeit führt. Diese Bewegungsmechanismen werden mit Ausnahme der Segmentrotation auch beim Dekamethylcyclopentasiloxan gefunden. Es wird eine Gegenüberstellung der experimentellen Daten der beiden hier untersuchten Systeme und eines polymeren Dimethylsiloxans gegeben. Dabei ist als interessantes Ergebnis hervorzuheben, daß die Methylgruppenrotation im Hexamethyldisiloxan die stärkste Behinderung erfährt.

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Summary In this experiment the longitudinal proton relaxation timesT ₁ of hexamethyldisiloxane and decamethylcyclopen-tasiloxane were measured in the temperature range from about 20 K up to 300 K. Three motional mechanisms, the methyl group rotation about the C₃-axis, the segmental rotation about the Si-O-bond and a motional process, not yet identified, which leads to a discontinuity ofT ₁ have been found to be responsible for the spin-lattice relaxation of hexamethyldisiloxane in this temperature range. With the exception of segmental rotation these motional processes also determine the spin-lattice relaxation of decamethylcyclopentasiloxane. A comparison of experimental data of the two systems actually investigated and a polymeric dimethylsiloxane is presented, showing the methyl group rotation being most strongly hindered in the case of hexamethyldisiloxane.

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Mit 4 Abbildungen und 1 Tabelle     

Die Hydrohalogenierung von Hexaphenyldigerman und die Schwingungsspektren einiger Ge2(C6H5) n X6−n -Verbindungen

The reactions of Ge₂(C₆H₅)₆ with HCl and HBr lead in nearly quantitative yields to the 1,1,2,2-tetrahalo derivatives Cl₂(C₆H₅)GeGe(C₆H₅)Cl₂ (I) and Br₂(C₆H₅)GeGe(C₆H₅)Br₂ (II), resp. The Si?Ge bond of (C₆H₅)₃SiGe(C₆H₅)₃ is cleaved under the conditions of hydrohalogenation. The vibrational spectra of Ge₂Br₆, Ge₂(C₆H₅)₆, I, and II are reported. The influence of vibrational coupling on ν GeGe in these compounds is discussed in detail, including vibrational calculations.     

High precision measurements of the hyperfine structure of seven metastable atomic states of57Fe by laser-Rf double-resonance

The hyperfine structure of the metastable atomic states (3d ⁷4s)⁵ F _2,3,4,5 and (3d ⁷ 4s)³ F _2,3,4 of⁵⁷Fe has been measured using theABMR- LIRF method (atomic beam magnetic resonance detected by laser induced resonance fluorescence). From these measurements the following hfs constantsA of the magnetic dipole interaction have been obtained (corrected for second order effects):A(⁵ F ₂)=55.994(7) MHzA(⁵ F ₃)=69.632(5) MHzA(⁵ F ₄)=78.435(4) MHzA(⁵ F ₅)=87.246(3) MHzA(³ F ₂)=143.328(4) MHzA(³ F ₃)=50.602(10) MHzA(³ F ₄)=13.456(5) MHz     

Gleichverteilung und Quadratwurzelschnecke

A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.

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Mit 2 Abbildungen

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Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet     

Eine Topologie auf der Menge der endlichdimensionalen nichtassoziativen Algebren über einem lokalen Körper

Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set of nonassociative algebras of a fixed dimensionr< over a local fieldF. We obtain a space, which is notT ₁. If the trivial algebra is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF ^*; forr3 the space is notT ₁. The set of division algebras is open in.     

Maße für gerichtete Geraden und nicht-symmetrische Pseudometriken in der Ebene II

We continue our investigations started in a paper with the same title. The -length of a curve defined in this paper can be written as an integral along the curve. Furthermore, we determine necessary and sufficient conditions for the existence of a measure of orientated lines which generates a given non-symmetric pseudo-metric.

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Herrn Prof. Dr. H.-J. Kanold zum 65. Geburtstag gewidmet     

Ein asymptotischer Ausdruck für eine zahlentheoretische Funktion

Arithmetic formulae and an asymptotic expression for the order of magnitude of the arithmetic function ged (s, n) and of a generalisation of it are derived.     

LP-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II

This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where denotes the Laplacian, a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain L^P-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems.     

Der quadratfreie Kern der Eulerschen φ-Funktion

It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers.